The present invention relates generally to the field of digital signal processing, and more particularly to the detection and characterization of Gaussian pulses.
In the field of digital signal processing there is often a need to detect a signal pulse in a transmission medium, such as an electrical cable or optical fiber, or an electronic or optical device. For example, in electronic or optical systems, when a signal encounters a change in impedance in the transmission medium, a partial reflectance of the signal occurs, decreasing the amplitude of the propagated signal. These impedance changes can substantially degrade the performance of a device or transmission medium, and so a great deal of effort has been spent detecting and analyzing such interconnect discontinuities.
One technique which has been used to great effect in this area is Time Domain Reflectometry (TDR). TDR involves measuring reflection in an unknown device or medium in comparison to reflection due to a standard impedance. In other words, TDR compares reflected energy to incident energy on a single-line transmission system. Known incident stimulus is applied to the standard impedance and intentionally propagated toward the unknown device or medium. Reflections from the unknown device or medium then propagate back to the source, and amplitude and time of the reflected signal(s) is compared to the incident stimulus. The reflected signal magnitude (and possibly the waveform) is a function of the incident signal magnitude and the nature of the impedance change. The time elapsed between the detection of the incident and the reflected signal is a function of the overall distance traveled and the velocity of propagation of the signal. Thus, by detecting and timing the reflected pulse with respect to the original pulse, the distance to an interconnect discontinuity may be determined. In this way, for example, a flaw, such as a kink, may be located precisely in the device or medium.
Fast sampling systems with TDR capability can be very useful for studying interconnect discontinuities. In a typical TDR system, a step generator, such as a switched current source, is used to generate a step pulse, which is propagated through a T-connector to a digitizer and the device under test (DUT) respectively. The reflected signal (from the DUT) is received by the digitizer and the superpositioned waveforms analyzed to determine the elapsed time, and to compare amplitude and waveform of the pulses.
However, there are a number of drawbacks to this approach. The use of a step function or signal is problematic because the steep rise of the leading edge of the step entails many high frequency signal components. In other words, the step signal is a wide bandwidth pulse. Transmission media and electronic and optical components behave differently for different frequencies, leading to such distorting effects as dispersion and dissipation of the pulse energy. The effect of dispersion is particularly troublesome for step pulses in TDR applications because the leading edge of the step is used to determine the timing of the pulse. The dispersion of high frequency components in the edge can smooth the edge to such a degree that precise timing of the reflected pulse may be difficult or even impossible.
Current systems developed to perform TDR with step pulses involve extremely high speed sampling and tend to be very expensive, costing on the order of one hundred thousand dollars each. The use of modulated Gaussian pulses could avoid many of the problems associated with step pulses in that Gaussian pulses are extremely smooth, have low bandwidth, and are particularly suitable for closed form analytic operations and representations. However, there are currently no known systems or methods to perform TDR with Gaussian pulses, due to difficulties in accurately detecting, timing, and characterizing Gaussian pulses in a noisy medium.
Therefore, systems and methods are desired to detect and characterize modulated Gaussian pulses in a noisy medium.
A system and method for detecting and characterizing Gaussian pulses is presented. A system and method for performing Time Domain Reflectometry (TDR) using Gaussian pulses is also described. The system may include a computer, comprising a CPU and a memory, wherein the memory is operable to store one or more software programs for performing TDR, and wherein the CPU is operable to execute the software programs. The system may also include an arbitrary waveform generator (AWG) coupled to the computer, and a digitizer coupled to the computer and the AWG. The system may be coupled to a Device or Medium, hereafter referred to as a Device Under Test (DUT). It should be noted that the DUT may be any kind of device, including a stand alone device, a PC board, an instrument, an electric or optical circuit, or an electronic or optical transmission medium, among others.
In the preferred embodiment, the computer system comprises a PCI eXtensions for Instrumentation (PXI) system which includes one or more PXI computer boards or cards plugged into a PXI backplane, such as a xe2x80x9cPC on a cardxe2x80x9d, housed in a PXI chassis. In other words, the PXI cards may comprise the memory and CPU which are operable to respectively store and execute one or more computer software programs implementing the present invention. The PXI system may also include or couple to a display, such as a monitor, for displaying visual information, such as results, to a user, as well as an I/O interface for receiving input and sending output to external systems or components. In one embodiment, the display may be comprised in the PXI chassis. In another embodiment, the display may be external to the PXI chassis. In one embodiment, the I/O interface may also be comprised on a PXI card.
The AWG may be operable to generate a Gaussian pulse and transmit the Gaussian pulse to the digitizer and to the Device Under Test (DUT). The DUT may be further operable to reflect at least a portion of the transmitted Gaussian pulse in the form of one or more reflected pulses to the digitizer. A digital signal containing a modulated Gaussian pulse and signal noise may be received, such as from the digitizer, from some other external system, or from the memory medium of the computer system. The signal may also include one or more reflected pulses. For example, in the TDR system described above, the AWG may generate a Gaussian pulse and transmit the Gaussian pulse to the digitizer and the Device Under Test (DUT). The DUT may reflect at least a portion of the transmitted Gaussian pulse to the digitizer, comprising the one or more reflected Gaussian pulses. The digitizer may receive and digitize the signal comprising the transmitted Gaussian pulse and the one or more reflected Gaussian pulses, and store the digitized signal in the memory.
An estimation of N Gaussian pulse parameters may be determined for a Gaussian pulse comprised in the signal, where N is greater than or equal to one. The Gaussian pulse parameters may include xcex1p (the inverse of the Gaussian pulse variance), tp (the Gaussian pulse time shift), and xcfx89p (the Gaussian pulse carrier frequency or base frequency). The pulse variance is related to the width of the Gaussian pulse. The pulse time shift is a measure of the time interval from some arbitrary origin to the peak of the Gaussian pulse. The pulse carrier frequency refers to the frequency of the modulation of the Gaussian pulse. In one embodiment, the estimation of Gaussian pulse parameters may be determined using any of various prior art techniques, such as the zoom-in approach, for example, which is well known in the art.
Once the estimation of the Gaussian pulse parameters is determined, a plurality of permutations of the estimated Gaussian Pulse parameters may be generated by adding or subtracting a small delta amount to or from each parameter value, producing a plurality of parameter sets representing a corresponding plurality of permuted Gaussian pulses or waveforms. If there are N estimated parameters, then M permutations of the N parameters may be generated, where M is greater than or equal to Nxe2x88x921. The original coarse estimated parameters and the M permutations comprise M+1 sets of parameters, such that for M=Nxe2x88x921, the minimal number of parameter sets (M+1)=N may be used to determine refined values for N parameter variables, described below. It should be noted that in some embodiments, the coarse estimation may not be used in determining the refined values.
In the preferred embodiment, M is greater than or equal to N so as to allow overdetermination of the N parameters. For example, where the pulse parameters are xcex1p, tp, and xcfx89p, N=3, and so M=3 permutation sets may be generated. It has been determined that, due to diminishing returns of increased overdetermination, in the preferred embodiment, letting M=N provides for the greatest benefit in refining the N estimated parameters.
In one embodiment, an inner or dot product, Qi, may be calculated between the received signal and each of the M permutations of the estimated Gaussian Pulse parameters, i.e., between the received signal and each of the M permuted Gaussian pulses or waveforms. This calculation is facilitated by the fact that for Gaussian pulses there is a closed form, or analytic, solution for the inner product. Said another way, each of the plurality of parameter sets may be used in the equation for Q, providing a corresponding plurality of inner product equations. The closed form equation of the inner product includes terms for the estimation parameters, as well as variables for the as yet undetermined parameters of the received Gaussian pulse.
The plurality of M inner products, Q, may be used to generate a corresponding plurality of M linear equations, each of which is a function of a respective one of the M estimation permutations and corresponding N parameter variables of the Gaussian pulse.
The plurality of linear equations may then be solved to overdetermine the parameters of the Gaussian pulse. It should be noted that in the case of three parameters or variables, a minimum of three linear equations could be solved to determine the variable values. However, by overdetermining the variable values through the use of more than the minimum number of linear equations, an xe2x80x9caveragingxe2x80x9d effect results, providing more accurate values for the parameters. Using the (over) determined parameters of the received Gaussian pulse, various analyses may be performed. For example, in the TDR system, a transmitted Gaussian pulse and one or more reflected pulses (from the DUT) may each be analyzed to characterize an interconnect discontinuity in the DUT. In one embodiment, the parameters may be used to determine the nature and magnitude of the discontinuity or the location of the discontinuity. For example, the characterized Gaussian pulses may be used to determine the transfer function of the discontinuity, or to calculate the impedance. As another example, the value of the time shift parameter tp for each pulse may be used to locate the interconnect discontinuity or flaw in the device or transmission medium.
In one embodiment, the method described above may be applied iteratively to a signal containing multiple Gaussian pulses, such as may be produced by the TDR system. In this embodiment, each time a pulse is detected and characterized, the characterized pulse may be subtracted from the signal, leaving a residue containing any remaining pulses. This residue may then be used as the input signal, and the next pulse detected and characterized. Again, the characterized pulse may be subtracted from the signal, leaving another residual signal, and so on, until all pulses of interested have been detected and characterized. Useful analyses may then be conducted on the resulting characterized pulses to extract useful information regarding the DUT, such as the number and nature of connection discontinuities therein.
Thus, by using various embodiments of the above-described method, a Gaussian pulse in a noisy signal may be detected and characterized. In one embodiment, the method may be used to distinguish between an original pulse and a plurality of reflected pulses in a TDR system, and to characterize connection discontinuities in the DUT or medium.